I am just beginning a research project on the study of closed orbits, specifically as related to hydrogen, and I wanted a little bit more information on what exactly makes something a "closed orbit". ...

In which sense is the configuration variable of a classical spin $SU(2)$? I can view a classical spin as a unit vector in $\mathbb{S}^2$ (2-dim. sphere), but it seems it is really given by a matrix ...

The general WKB approximation formula states that
$$
\int_a^b\sqrt{E_k-V(x)} = (k+1)\pi \text{ with } x \in [a,b]
$$
for a regular Schrödinger equation (without the $\hbar$ and such). However, in the ...

Let's have quasiclassical QM for central field $V(r)$. The Schroedinger equation for radial part of wavefunction $R_{n\ell}$ after substitution $u_{n\ell} = rR_{n\ell}$ takes the form
$$
u_{n\ell}{''} ...

I'm working on a numerical program which approximates the eigenvalues of a Schrödinger equation by making use of the WKB approximation formulas. For example, if the Schrödinger equation is
$$
y''(x) = ...

I find myself often puzzled with the different definitions one gives to "semiclassical limits" in the context of quantum mechanics, in other words limits that eventually turn quantum mechanics into ...

I've recently stumbled upon a semiclassical approximation to quantum field theory that I've never heard of and have a hard time understanding. Consider the Hamiltonian,
\begin{equation}
H = \frac{c}{ ...

I need help to find the energy eigen values of Hydrogen atom using WKB approach. So far I know, the radial equation is given by
$$\frac{1}{r^2} \frac{\partial }{\partial r} \left( r^2 \frac{\partial ...

Black hole evaporation is a result of calculating the expectation value of the stress-energy tensor of the state of the vacuum in certain spacetimes and then making a plausibility argument as to the ...

I'm trying to learn how to apply WKB. I asked a similar question already, but that question was related to finding the energies. Here, I would like to understand how to find the wave functions using ...

In many books I read about semiclassical approximation applied to the field of Bose-Einstein condensation.
But I don't understand what it really means.
For example I read that an expression like this
...

What are some important approximations, especially those that are state-of-the-art, used to approximate the many-body dynamics of atoms and molecules in the semiclassical regime? To be clear, I'm not ...

Preamble:
If one considers an ideal gas of non interacting charged particles of charge $q$ in a uniform magnetic field $\mathbf{B} = \mathbf{\nabla} \wedge \mathbf{A}$, then the classical partition ...

I am trying to calculate atom - light (EM field) interaction Hamiltonian, and the results I get seem to me rather unphysical - I get some nonzero matrix elements which should not be there. Please, can ...

The Gutzwiller trace is about
$$ d(E)=d_{0} (E)+ \sum_{p.o}A_{p}Cos(S(E)\ell_{p}) $$
and $ \ell_{p} $ are the length of the orbit.
However my question is, how can one derive the length of the orbit ...

Suppose we have two black holes of radius $R_b$ orbiting at a distance $R_r$. I believe semi-classical approximations describe correctly the case where $R_r$ is much larger than the average black body ...

This site says that "it has recently been proven that the photoelectric effect can be interpreted classically (or at least semi-classically) in non-particle, wavelike terms". Is anyone familiar with ...

If the potential is bounded below $ V(x)=V(-x) \ge a $ for some real number $a$, and we can be sure that as $ x\rightarrow \infty $ we know that $ V(x) \ge 0 $ then does it mean that the energies for ...

let be the Hamiltonian of a surface $ H= g_{a,b} p^{a}p^{b} $ (Einstein summation assumed) my question is if although the space time is curved then can we use the WKB approximation to get the quantum ...